Local and nonlocal symmetries for nonlinear telegraph equation

2005 ◽  
Vol 46 (2) ◽  
pp. 023505 ◽  
Author(s):  
G. W. Bluman ◽  
Temuerchaolu ◽  
R. Sahadevan
Keyword(s):  
Telegraph Equation ◽  
Nonlocal Symmetries ◽  
Nonlinear Telegraph Equation

Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries

1990 ◽  
Vol 1 (3) ◽  
pp. 217-223 ◽  
Author(s):  
G. W. Bluman ◽  
S. Kumei
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Telegraph Equation ◽  
Partial Differential ◽  
Nonlocal Symmetries ◽  
Nonlinear Heat Conduction Equation ◽  
Local Symmetries ◽  
Nonlinear Telegraph Equation ◽  
The Given

An algorithm is presented to linearize nonlinear partial differential equations by non-invertible mappings. The algorithm depends on finding nonlocal symmetries of the given equations which are realized as appropriate local symmetries of a related auxiliary system. Examples include the Hopf-Cole transformation and the linearizations of a nonlinear heat conduction equation, a nonlinear telegraph equation, and the Thomas equations.

Continuous symmetries of the discrete nonlinear telegraph equation

1999 ◽  
Vol 10 (3) ◽  
pp. 265-284 ◽  
Author(s):  
M. S. ODY ◽  
A. K. COMMON ◽  
M. I. SOBHY
Keyword(s):  
Initial Data ◽  
Difference Equations ◽  
Numerical Scheme ◽  
Telegraph Equation ◽  
Lie Symmetries ◽  
Discrete Equation ◽  
Symmetry Reductions ◽  
Nonlinear Telegraph Equation ◽  
Continuous Symmetries

The method of classical Lie symmetries, generalised to differential-difference equations by Quispel, Capel and Sahadevan, is applied to the discrete nonlinear telegraph equation. The symmetry reductions thus obtained are compared with analogous results for the continuous telegraph equation. Some of these ‘continuous’ reductions are used to provide initial data for a numerical scheme which attempts to solve the corresponding discrete equation.

scholarly journals Travelling Wave solutions of hyperbolic Telegraph equation by Tanh method

2021 ◽  
Vol 12 (2) ◽  
pp. 3032-3035
Author(s):  
Anjali Verma, Et. al.
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Telegraph Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Tanh Method ◽  
Convenient Approach ◽  
Nonlinear Telegraph Equation

Tanh method is utilized to find travelling solutions of second order nonlinear Telegraph equation. As a result, we attain dissimilar travelling wave solutions. Our aim is to show that this method is most efficient and convenient approach for verdict travelling wave solutions of nonlinear differential equations. For calculation the software MAPLE is used.

scholarly journals Exact solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation via the first integral method

2012 ◽  
Vol 17 (4) ◽  
pp. 481-488 ◽  
Author(s):  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Exact Solutions ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Telegraph Equation ◽  
First Integral Method ◽  
Wave Solutions ◽  
Nonlinear Telegraph Equation

In this article we find the exact traveling wave solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation by using the first integral method. This method is based on the theory of commutative algebra. This method can be applied to nonintegrable equations as well as to integrable ones.

Application of a Homogeneous Balance Method to Exact Solutions of Nonlinear Fractional Evolution Equations

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
H. Jafari ◽  
H. Tajadodi ◽  
D. Baleanu
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Telegraph Equation ◽  
Fisher Equation ◽  
Fractional Evolution Equations ◽  
Liouville Derivative ◽  
Nonlinear Telegraph Equation ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

The fractional Fan subequation method of the fractional Riccati equation is applied to construct the exact solutions of some nonlinear fractional evolution equations. In this paper, a powerful algorithm is developed for the exact solutions of the modified equal width equation, the Fisher equation, the nonlinear Telegraph equation, and the Cahn–Allen equation of fractional order. Fractional derivatives are described in the sense of the modified Riemann–Liouville derivative. Some relevant examples are investigated.

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